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Fractions & Percentages of Quantities (SQA National 5 Applications of Mathematics): Revision Note

Exam code: X844 75

Written by: Dan Finlay

Reviewed by: Roger B

Updated on 1 December 2025

Fractions of quantities

How do I find a fraction of a quantity?

STEP 1
Divide the quantity by the denominator
- e.g. $\frac{1}{5}$ of $60$ is found by $60 \div 5 = 12$
STEP 2
Multiply by the numerator
- e.g. $\frac{2}{5}$ of $60$ is found by $12 \times 2 = 24$

Examiner Tips and Tricks

On Paper 2, you can just multiply the fraction by the quantity in your calculator.

$\frac{2}{5} \times 60 = 24$

Worked Example

A rugby stadium can seat 2000 people.

For a particular game, $\frac{11}{20}$ of the seats are filled.

How many seats are filled?

Answer:

STEP 1

Divide the number of seats by 20

$2000 \div 20 = 100$

STEP 2

Multiply by 11

$100 \times 11 = 1100$

1100 seats

Percentages of quantities

How do I find a percentage of a quantity?

With a calculator

STEP 1
Find the decimal multiplier by converting the percentage to a decimal
- e.g. 12% = 12 ÷ 100 = 0.12
STEP 2
Multiply the quantity by the multiplier
- e.g. 12% of 650 is 0.12 × 650 = 78

Worked Example

Lachlan donates 8% of his net pay to charity each month.

In June, Lachlan's net pay is £2,354.

How much does Lachlan donate to charity in June?

Answer:

STEP 1

Change 8% to a decimal

$8 % = 8 \div 100 = 0.08$

STEP 2

Multiply by Lachlan's net pay

$0.08 \times 2354 = 188.32$

£188.32

Without a calculator

The calculator method works without a calculator
- You just need to multiply by a decimal without a calculator
It might be quicker to find easy percentages first
- You can do this by thinking about the equivalent fraction

Percentage	Fraction	Method
10%	$\frac{1}{10}$	Divide the quantity by 10
50%	$\frac{1}{2}$	Divide the quantity by 2
25%	$\frac{1}{4}$	Divide the quantity by 4
5%	$\frac{1}{20}$	Divide the quantity by 20 (or divide by 10 and then divide by 2)
20%	$\frac{1}{5}$	Divide the quantity by 5 (or divide by 10 and then multiply by 2)
75%	$\frac{3}{4}$	Divide the quantity by 4 and multiply by 3
1%	$\frac{1}{100}$	Divide the quantity by 100

You can find other percentages by using easier ones
- 30% is 3 × 10%
- 2.5% is half of 5%
- 15% is 10% + 5%

Worked Example

A school in Auchtertool has 340 students.

45% of students study Applications of Mathematics.

Without using a calculator, find the number of students in the school that study Applications of Mathematics.

Answer:

Find 10%

$10 % of 340 = 340 \div 10 = 34$

Multiply 10% by 4 to find 40%

$40 % of 340 = 4 \times 34 = 136$

Halve 10% to find 5%

$5 % of 340 = 34 \div 2 = 17$

Add 40% and 5% together to find 45%

$45 % of 340 = 136 + 17 = 153$

153 students

A quantity as a percentage of another

How do I write one quantity as a percentage of another quantity?

With a calculator

STEP 1
Write the first quantity as a fraction of the second quantity
- e.g. 17 out 25 marks is $\frac{17}{25}$
STEP 2
Convert to a percentage by multiplying by 100
- e.g. $\frac{17}{25} \times 100 = 68$
- 17 is 68% of 25

Without a calculator

You can still use the calculator method by finding the fraction of 100%
- You need to divide 100% by the denominator
  - $100 % \div 25 = 4 %$
- and then multiply by the numerator
  - $17 \times 4 % = 68 %$
It helps if you simplify the fraction first
- e.g. 12 out of 30 is $\frac{12}{30}$
  - $100 % \div 30$ can be difficult without a calculator
- Simplify to $\frac{12 \div 6}{30 \div 6} = \frac{2}{5}$
  - $100 % \div 5 = 20 %$
  - $2 \times 20 % = 40 %$
- 12 is 40% of 30

Worked Example

Catriona has 60 minutes to complete a test. She finishes it in 51 minutes.

Without using a calculator, find the percentage of the time allowed used by Catriona.

Answer:

Write it as a fraction

51 out of 60 minutes is $\frac{51}{60}$

Simplify the fraction

$\frac{51 \div 3}{60 \div 3} = \frac{17}{20}$

Divide 100% by the denominator

$100 % \div 20 = 5 %$

Multiply by the numerator

$17 \times 5 % = 85 %$

Catriona used 85% of the time allowed

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Fractions & Percentages of Quantities (SQA National 5 Applications of Mathematics): Revision Note

Fractions of quantities

How do I find a fraction of a quantity?

Examiner Tips and Tricks

Worked Example

Percentages of quantities

How do I find a percentage of a quantity?

With a calculator

Worked Example

Without a calculator

Worked Example

A quantity as a percentage of another

How do I write one quantity as a percentage of another quantity?

With a calculator

Without a calculator

Worked Example

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

Author: Dan Finlay

Reviewer: Roger B